qlc

Query Interface to Mnesia, ETS, Dets, etc

The qlc module provides a query interface to Mnesia, ETS,
Dets and other data structures that implement an iterator style
traversal of objects.

Overview

The qlc module implements a query interface to QLC
tables. Typical QLC tables are ETS, Dets, and Mnesia
tables. There is also support for user defined tables, see the
Implementing a QLC
table section.
A query is stated using
Query List Comprehensions (QLCs). The answers to a
query are determined by data in QLC tables that fulfill the
constraints expressed by the QLCs of the query. QLCs are similar
to ordinary list comprehensions as described in the Erlang
Reference Manual and Programming Examples except that variables
introduced in patterns cannot be used in list expressions. In
fact, in the absence of optimizations and options such as
cache and unique (see below), every QLC free of
QLC tables evaluates to the same list of answers as the
identical ordinary list comprehension.

While ordinary list comprehensions evaluate to lists, calling
qlc:q/1,2 returns a Query
Handle. To obtain all the answers to a query, qlc:eval/1,2 should be called with the
query handle as first argument. Query handles are essentially
functional objects ("funs") created in the module calling q/1,2.
As the funs refer to the module's code, one should
be careful not to keep query handles too long if the module's
code is to be replaced.
Code replacement is described in the Erlang Reference
Manual. The list of answers can also be traversed in
chunks by use of a Query Cursor. Query cursors are
created by calling qlc:cursor/1,2 with a query handle as
first argument. Query cursors are essentially Erlang processes.
One answer at a time is sent from the query cursor process to
the process that created the cursor.

Syntax

Syntactically QLCs have the same parts as ordinary list
comprehensions:

[Expression || Qualifier1, Qualifier2, ...]

Expression (the template) is an arbitrary
Erlang expression. Qualifiers are either filters or
generators. Filters are Erlang expressions returning
bool(). Generators have the form
Pattern <- ListExpression, where
ListExpression is an expression evaluating to a query
handle or a list. Query handles are returned from
qlc:table/2, qlc:append/1,2, qlc:sort/1,2,
qlc:keysort/2,3, qlc:q/1,2, and
qlc:string_to_handle/1,2,3.

Evaluation

The evaluation of a query handle begins by the inspection of
options and the collection of information about tables. As a
result qualifiers are modified during the optimization phase.
Next all list expressions are evaluated. If a cursor has been
created evaluation takes place in the cursor process. For those
list expressions that are QLCs, the list expressions of the
QLCs' generators are evaluated as well. One has to be careful if
list expressions have side effects since the order in which list
expressions are evaluated is unspecified. Finally the answers
are found by evaluating the qualifiers from left to right,
backtracking when some filter returns false, or
collecting the template when all filters return true.

Filters that do not return bool() but fail are handled
differently depending on their syntax: if the filter is a guard
it returns false, otherwise the query evaluation fails.
This behavior makes it possible for the qlc module to do
some optimizations without affecting the meaning of a query. For
example, when testing some position of a table and one or more
constants for equality, only
the objects with equal values are candidates for further
evaluation. The other objects are guaranteed to make the filter
return false, but never fail. The (small) set of
candidate objects can often be found by looking up some key
values of the table or by traversing the table using a match
specification. It is necessary to place the guard filters
immediately after the table's generator, otherwise the candidate
objects will not be restricted to a small set. The reason is
that objects that could make the query evaluation fail must not
be excluded by looking up a key or running a match
specification.

Join

The qlc module supports fast join of two query handles.
Fast join is possible if some position P1 of one query
handler and some position P2 of another query handler are
tested for equality. Two fast join methods have been
implemented:

Lookup join traverses all objects of one query handle and
finds objects of the other handle (a QLC table) such that the
values at P1 and P2 match or compare equal.
The qlc module does not create
any indices but looks up values using the key position and
the indexed positions of the QLC table.
Merge join sorts the objects of each query handle if
necessary and filters out objects where the values at
P1 and P2 do not compare equal. If there are
many objects with the same value of P2 a temporary
file will be used for the equivalence classes.

The qlc module warns at compile time if a QLC
combines query handles in such a way that more than one join is
possible. In other words, there is no query planner that can
choose a good order between possible join operations. It is up
to the user to order the joins by introducing query handles.

The join is to be expressed as a guard filter. The filter must
be placed immediately after the two joined generators, possibly
after guard filters that use variables from no other generators
but the two joined generators. The qlc module inspects
the operands of
=:=/2, ==/2, is_record/2, element/2,
and logical operators (and/2, or/2,
andalso/2, orelse/2, xor/2) when
determining which joins to consider.

Common options

The following options are accepted by cursor/2,
eval/2, fold/4, and info/2:

{cache_all, Cache} where Cache is
equal to ets or list adds a
{cache, Cache} option to every list expression
of the query except tables and lists. Default is
{cache_all, no}. The option cache_all is
equivalent to {cache_all, ets}.
{max_list_size, MaxListSize} where MaxListSize is the
size in bytes of terms on the external format. If the
accumulated size of collected objects exceeds
MaxListSize the objects are written onto a temporary
file. This option is used by the {cache, list}
option as well as by the merge join method. Default is
512*1024 bytes.
{tmpdir_usage, TmpFileUsage} determines the
action taken when qlc is about to create temporary
files on the directory set by the tmpdir option. If the
value is not_allowed an error tuple is returned,
otherwise temporary files are created as needed. Default is
allowed which means that no further action is taken.
The values info_msg, warning_msg, and
error_msg mean that the function with the corresponding
name in the module error_logger is called for printing
some information (currently the stacktrace).
{tmpdir, TempDirectory} sets the directory used by
merge join for temporary files and by the
{cache, list} option. The option also overrides
the tmpdir option of keysort/3 and
sort/2. The default value is "" which means that
the directory returned by file:get_cwd() is used.
{unique_all, true} adds a
{unique, true} option to every list expression of
the query. Default is {unique_all, false}. The
option unique_all is equivalent to
{unique_all, true}.

Getting started

As already mentioned
queries are stated in the list comprehension syntax as described
in the Erlang
Reference Manual. In the following some familiarity
with list comprehensions is assumed. There are examples in
Programming
Examples that can get you started. It should be
stressed that list comprehensions do not add any computational
power to the language; anything that can be done with list
comprehensions can also be done without them. But they add a
syntax for expressing simple search problems which is compact
and clear once you get used to it.

Many list comprehension expressions can be evaluated by the
qlc module. Exceptions are expressions such that
variables introduced in patterns (or filters) are used in some
generator later in the list comprehension. As an example
consider an implementation of lists:append(L):
[X ||Y <- L, X <- Y].
Y is introduced in the first generator and used in the second.
The ordinary list comprehension is normally to be preferred when
there is a choice as to which to use. One difference is that
qlc:eval/1,2 collects answers in a list which is finally
reversed, while list comprehensions collect answers on the stack
which is finally unwound.

What the qlc module primarily adds to list
comprehensions is that data can be read from QLC tables in small
chunks. A QLC table is created by calling qlc:table/2.
Usually qlc:table/2 is not called directly from the query
but via an interface function of some data structure. There are
a few examples of such functions in Erlang/OTP:
mnesia:table/1,2, ets:table/1,2, and
dets:table/1,2. For a given data structure there can be
several functions that create QLC tables, but common for all
these functions is that they return a query handle created by
qlc:table/2. Using the QLC tables provided by OTP is
probably sufficient in most cases, but for the more advanced
user the section Implementing a QLC
table describes the implementation of a function
calling qlc:table/2.

Besides qlc:table/2 there are other functions that
return query handles. They might not be used as often as tables,
but are useful from time to time. qlc:append traverses
objects from several tables or lists after each other. If, for
instance, you want to traverse all answers to a query QH and
then finish off by a term {finished}, you can do that by
calling qlc:append(QH, [{finished}]). append first
returns all objects of QH, then {finished}. If there is
one tuple {finished} among the answers to QH it will be
returned twice from append.

As another example, consider concatenating the answers to two
queries QH1 and QH2 while removing all duplicates. The means to
accomplish this is to use the unique option:

qlc:q([X || X <- qlc:append(QH1, QH2)], {unique, true})

The cost is substantial: every returned answer will be stored
in an ETS table. Before returning an answer it is looked up in
the ETS table to check if it has already been returned. Without
the unique options all answers to QH1 would be returned
followed by all answers to QH2. The unique options keeps
the order between the remaining answers.

If the order of the answers is not important there is the
alternative to sort the answers uniquely:

qlc:sort(qlc:q([X || X <- qlc:append(QH1, QH2)], {unique, true})).

This query also removes duplicates but the answers will be
sorted. If there are many answers temporary files will be used.
Note that in order to get the first unique answer all answers
have to be found and sorted. Both alternatives find duplicates
by comparing answers, that is, if A1 and A2 are answers found in
that order, then A2 is a removed if A1 == A2.

To return just a few answers cursors can be used. The following
code returns no more than five answers using an ETS table for
storing the unique answers:

The qlc module will evaluate this differently depending on
the query
handles QH1 and QH2. If, for example, X2 is
matched against the key of a QLC table the lookup join method
will traverse the objects of QH2 while looking up key
values in the table. On the other hand, if neither X2 nor
Y2 is matched against the key or an indexed position of a
QLC table, the merge join method will make sure that QH1
and QH2 are both sorted on position 2 and next do the
join by traversing the objects one by one.

The join option can be used to force the qlc module
to use a
certain join method. For the rest of this section it is assumed
that the excessively slow join method called "nested loop" has
been chosen:

In this case the filter will be applied to every possible pair
of answers to QH1 and QH2, one at a time. If there are M answers
to QH1 and N answers to QH2 the filter will be run M*N
times.

If QH2 is a call to the function for gb_trees as defined
in the Implementing
a QLC table section, gb_table:table/1, the
iterator for the gb-tree will be initiated for each answer to
QH1 after which the objects of the gb-tree will be returned one
by one. This is probably the most efficient way of traversing
the table in that case since it takes minimal computational
power to get the following object. But if QH2 is not a table but
a more complicated QLC, it can be more efficient use some RAM
memory for collecting the answers in a cache, particularly if
there are only a few answers. It must then be assumed that
evaluating QH2 has no side effects so that the meaning of the
query does not change if QH2 is evaluated only once. One way of
caching the answers is to evaluate QH2 first of all and
substitute the list of answers for QH2 in the query. Another way
is to use the cache option. It is stated like this:

QH2' = qlc:q([X || X <- QH2], {cache, ets})

or just

QH2' = qlc:q([X || X <- QH2], cache)

The effect of the cache option is that when the
generator QH2' is run the first time every answer is stored in
an ETS table. When next answer of QH1 is tried, answers to QH2'
are copied from the ETS table which is very fast. As for the
unique option the cost is a possibly substantial amount
of RAM memory. The {cache, list} option offers the
possibility to store the answers in a list on the process heap.
While this has the potential of being faster than ETS tables
since there is no need to copy answers from the table it can
often result in slower evaluation due to more garbage
collections of the process' heap as well as increased RAM memory
consumption due to larger heaps. Another drawback with cache
lists is that if the size of the list exceeds a limit a
temporary file will be used. Reading the answers from a file is
very much slower than copying them from an ETS table. But if the
available RAM memory is scarce setting the limit to some low value is an
alternative.

There is an option cache_all that can be set to
ets or list when evaluating a query. It adds a
cache or {cache, list} option to every list
expression except QLC tables and lists on all levels of the
query. This can be used for testing if caching would improve
efficiency at all. If the answer is yes further testing is
needed to pinpoint the generators that should be cached.

Implementing a QLC table

As an example of
how to use the qlc:table/2
function the implementation of a QLC table for the gb_trees module is given:

TF is the traversal function. The qlc module
requires that there is a way of traversing all objects of the
data structure; in gb_trees there is an iterator function
suitable for that purpose. Note that for each object returned a
new fun is created. As long as the list is not terminated by
[] it is assumed that the tail of the list is a nullary
function and that calling the function returns further objects
(and functions).

The lookup function is optional. It is assumed that the lookup
function always finds values much faster than it would take to
traverse the table. The first argument is the position of the
key. Since qlc_next returns the objects as
{Key, Value} pairs the position is 1. Note that the lookup
function should return {Key, Value} pairs, just as the
traversal function does.

The format function is also optional. It is called by
qlc:info to give feedback at runtime of how the query
will be evaluated. One should try to give as good feedback as
possible without showing too much details. In the example at
most 7 objects of the table are shown. The format function
handles two cases: all means that all objects of the
table will be traversed; {lookup, 1, KeyValues}
means that the lookup function will be used for looking up key
values.

Whether the whole table will be traversed or just some keys
looked up depends on how the query is stated. If the query has
the form

qlc:q([T || P <- LE, F])

and P is a tuple, the qlc module analyzes P and F in
compile time to find positions of the tuple P that are tested
for equality to constants. If such a position at runtime turns
out to be the key position, the lookup function can be used,
otherwise all objects of the table have to be traversed. It is
the info function InfoFun that returns the key position.
There can be indexed positions as well, also returned by the
info function. An index is an extra table that makes lookup on
some position fast. Mnesia maintains indices upon request,
thereby introducing so called secondary keys. The qlc
module prefers to look up objects using the key before secondary
keys regardless of the number of constants to look up.

Key equality

In Erlang there are two operators for testing term equality,
namely ==/2 and =:=/2. The difference between them
is all about the integers that can be represented by floats. For
instance, 2 == 2.0 evaluates to
true while 2 =:= 2.0 evaluates to false.
Normally this is a minor issue, but the qlc module cannot
ignore the difference, which affects the user's choice of
operators in QLCs.

If the qlc module can find out at compile time that some
constant is free of integers, it does not matter which one of
==/2 or =:=/2 is used:

In the example the ==/2 operator has been handled
exactly as =:=/2 would have been handled. On the other
hand, if it cannot be determined at compile time that some
constant is free of integers and the table uses =:=/2
when comparing keys for equality (see the option key_equality), the
qlc module will not try to look up the constant. The
reason is that there is in the general case no upper limit on
the number of key values that can compare equal to such a
constant; every combination of integers and floats has to be
looked up:

Lookup join is handled analogously to lookup of constants in a
table: if the join operator is ==/2 and the table where
constants are to be looked up uses =:=/2 when testing
keys for equality, the qlc module will not consider
lookup join for that table.

Creates a query cursor and
makes the calling process the owner of the cursor. The
cursor is to be used as argument to next_answers/1,2
and (eventually) delete_cursor/1. Calls
erlang:spawn_opt to spawn and link a process which
will evaluate the query handle. The value of the option
spawn_options is used as last argument when calling
spawn_opt. The default value is [link].

Calls Function on successive answers to
the query handle together with an extra argument
AccIn. The query handle and the function
are evaluated in the calling process.
Function must return a new accumulator
which is passed to the next call.
Acc0 is returned if there are no answers
to the query handle.

format_error(Error) -> Chars

Returns a descriptive string in English of an error tuple
returned by some of the functions of the qlc module
or the parse transform. This function is mainly used by the
compiler invoking the parse transform.

Returns information about a
query handle. The information describes the simplifications
and optimizations that are the results of preparing the
query for evaluation. This function is probably useful
mostly during debugging.

The information has the form of an Erlang expression where
QLCs most likely occur. Depending on the format functions of
mentioned QLC tables it may not be absolutely accurate.

The default is to return a sequence of QLCs in a block, but
if the option {flat, false} is given, one single
QLC is returned. The default is to return a string, but if
the option {format, abstract_code} is given,
abstract code is returned instead. In the abstract code
port identifiers, references, and pids are represented by
strings. The default is to return
all elements in lists, but if the
{n_elements, NElements} option is given, only a
limited number of elements are returned. The default is to
show all of objects and match specifications, but if the
{depth, Depth} option is given, parts of terms
below a certain depth are replaced by '...'.

In this example the query list comprehension V2 has
been inserted to show the joined generators and the join
method chosen. A convention is used for lookup join: the
first generator (G2) is the one traversed, the second
one (G1) is the table where constants are looked up.

next_answers(QueryCursor, NumberOfAnswers) -> Answers | Error

Returns some or all of the remaining answers to a query
cursor. Only the owner of QueryCursor can
retrieve answers.

The optional argument NumberOfAnswersdetermines the
maximum number of answers returned. The default value is
10. If less than the requested number of answers is
returned, subsequent calls to next_answers will
return [].

Returns a query handle for a query
list comprehension. The query list comprehension must be the
first argument to qlc:q/1,2 or it will be evaluated
as an ordinary list comprehension. It is also necessary to
add the line

-include_lib("stdlib/include/qlc.hrl").

to the source file. This causes a parse transform to
substitute a fun for the query list comprehension. The
(compiled) fun will be called when the query handle is
evaluated.

When calling qlc:q/1,2 from the Erlang shell the
parse transform is automatically called. When this happens
the fun substituted for the query list comprehension is not
compiled but will be evaluated by erl_eval(3). This
is also true when expressions are evaluated by means of
file:eval/1,2 or in the debugger.

To be very explicit, this will not work:

...
A = [X || {X} <- [{1},{2}]],
QH = qlc:q(A),
...

The variable A will be bound to the evaluated value
of the list comprehension ([1,2]). The compiler
complains with an error message ("argument is not a query
list comprehension"); the shell process stops with a
badarg reason.

q(QLC) is equivalent to
q(QLC, []).

The {cache, ets} option can be used to cache
the answers to a query list comprehension. The answers are
stored in one ETS table for each cached query list
comprehension. When a cached query list comprehension is
evaluated again, answers are fetched from the table without
any further computations. As a consequence, when all answers
to a cached query list comprehension have been found, the
ETS tables used for caching answers to the query list
comprehension's qualifiers can be emptied. The option
cache is equivalent to {cache, ets}.

The {cache, list} option can be used to cache
the answers to a query list comprehension just like
{cache, ets}. The difference is that the answers
are kept in a list (on the process heap). If the answers
would occupy more than a certain amount of RAM memory a
temporary file is used for storing the answers. The option
max_list_size sets the limit in bytes and the temporary
file is put on the directory set by the tmpdir option.

The cache option has no effect if it is known that
the query list comprehension will be evaluated at most once.
This is always true for the top-most query list
comprehension and also for the list expression of the first
generator in a list of qualifiers. Note that in the presence
of side effects in filters or callback functions the answers
to query list comprehensions can be affected by the
cache option.

The {unique, true} option can be used to remove
duplicate answers to a query list comprehension. The unique
answers are stored in one ETS table for each query list
comprehension. The table is emptied every time it is known
that there are no more answers to the query list
comprehension. The option unique is equivalent to
{unique, true}. If the unique option is
combined with the {cache, ets} option, two ETS
tables are used, but the full answers are stored in one
table only. If the unique option is combined with the
{cache, list} option the answers are sorted
twice using keysort/3; once to remove duplicates, and
once to restore the order.

The cache and unique options apply not only
to the query list comprehension itself but also to the
results of looking up constants, running match
specifications, and joining handles.

In this example the cached results of the merge join are
traversed for each value of A. Note that without the
cache option the join would have been carried out
three times, once for each value of A

sort/1,2 and keysort/2,3 can also be used for
caching answers and for removing duplicates. When sorting
answers are cached in a list, possibly stored on a temporary
file, and no ETS tables are used.

Sometimes (see qlc:table/2 below) traversal
of tables can be done by looking up key values, which is
assumed to be fast. Under certain (rare) circumstances it
could happen that there are too many key values to look up.
The
{max_lookup, MaxLookup} option can then be used
to limit the number of lookups: if more than
MaxLookup lookups would be required no lookups are
done but the table traversed instead. The default value is
infinity which means that there is no limit on the
number of keys to look up.

In this example using the gb_table module from the
Implementing a
QLC table section there are six keys to look up:
{1,a}, {1,b}, {1,c}, {2,a},
{2,b}, and {2,c}. The reason is that the two
elements of the key {X, Y} are compared separately.

The {lookup, true} option can be used to ensure
that the qlc module will look up constants in some
QLC table. If there
are more than one QLC table among the generators' list
expressions, constants have to be looked up in at least one
of the tables. The evaluation of the query fails if there
are no constants to look up. This option is useful in
situations when it would be unacceptable to traverse all
objects in some table. Setting the lookup option to
false ensures that no constants will be looked up
({max_lookup, 0} has the same effect). The
default value is any which means that constants will
be looked up whenever possible.

The {join, Join} option can be used to ensure
that a certain join method will be used:
{join, lookup} invokes the lookup join method;
{join, merge} invokes the merge join method; and
{join, nested_loop} invokes the method of
matching every pair of objects from two handles. The last
method is mostly very slow. The evaluation of the query
fails if the qlc module cannot carry out the chosen
join method. The
default value is any which means that some fast join
method will be used if possible.

A string version of qlc:q/1,2. When the query handle
is evaluated the fun created by the parse transform is
interpreted by erl_eval(3). The query string is to be
one single query list comprehension terminated by a
period.

Returns a query handle for a
QLC table. In Erlang/OTP there is support for ETS, Dets and
Mnesia tables, but it is also possible to turn many other
data structures into QLC tables. The way to accomplish this
is to let function(s) in the module implementing the data
structure create a query handle by calling
qlc:table/2. The different ways to traverse the table
as well as properties of the table are handled by callback
functions provided as options to qlc:table/2.

The callback function TraverseFun is
used for traversing the table. It is to return a list of
objects terminated by either [] or a nullary fun to
be used for traversing the not yet traversed objects of the
table. Any other return value is immediately returned as
value of the query evaluation. Unary
TraverseFuns are to accept a match
specification as argument. The match specification is
created by the parse transform by analyzing the pattern of
the generator calling qlc:table/2 and filters using
variables introduced in the pattern. If the parse transform
cannot find a match specification equivalent to the pattern
and filters, TraverseFun will be called
with a match specification returning every object. Modules
that can utilize match specifications for optimized
traversal of tables should call qlc:table/2 with a
unary
TraverseFun while other modules can
provide a nullary
TraverseFun. ets:table/2 is an
example of the former; gb_table:table/1 in the
Implementing a
QLC table section is an example of the latter.

PreFun is a unary callback function
that is called once before the table is read for the first
time. If the call fails, the query evaluation fails.
Similarly, the nullary callback function
PostFun is called once after the table
was last read. The return value, which is caught, is
ignored. If PreFun has been called for a
table,
PostFun is guaranteed to be called for
that table, even if the evaluation of the query fails for
some reason. The order in which pre (post) functions for
different tables are evaluated is not specified. Other table
access than reading, such as calling
InfoFun, is assumed to be OK at any
time. The argument PreArgs is a list of
tagged values. Currently there are two tags,
parent_value and stop_fun, used by Mnesia for
managing transactions. The value of parent_value is
the value returned by ParentFun, or
undefined if there is no ParentFun.
ParentFun is called once just before the
call of
PreFun in the context of the process
calling
eval, fold, or
cursor. The value of stop_fun is a nullary fun
that deletes the cursor if called from the parent, or
undefined if there is no cursor.

The binary callback
function LookupFun is used for looking
up objects in the table. The first argument
Position is the key position or an
indexed position and the second argument
Keys is a sorted list of unique values.
The return value is to be a list of all objects (tuples)
such that the element at Position is a member of
Keys. Any other return value is
immediately returned as value of the query evaluation.
LookupFun is called instead of
traversing the table if the parse transform at compile time
can find out that the filters match and compare the element
at Position in such a way that only
Keys need to be looked up in order to
find all potential answers. The key position is obtained by
calling
InfoFun(keypos) and the indexed
positions by calling
InfoFun(indices). If the key position
can be used for lookup it is always chosen, otherwise the
indexed position requiring the least number of lookups is
chosen. If there is a tie between two indexed positions the
one occurring first in the list returned by
InfoFun is chosen. Positions requiring
more than max_lookup
lookups are ignored.

The unary callback function InfoFun is
to return information about the table. undefined
should be returned if the value of some tag is unknown:

indices. Returns a list of indexed
positions, a list of positive integers.
is_unique_objects. Returns true if
the objects returned by TraverseFun are unique.
keypos. Returns the position of the table's
key, a positive integer.
is_sorted_key. Returns true if
the objects returned by TraverseFun are sorted
on the key.
num_of_objects. Returns the number of
objects in the table, a non-negative integer.

The unary callback function FormatFun
is used by qlc:info/1,2
for displaying the call that created the table's query
handle. The default value, undefined, means that
info/1,2 displays a call to '$MOD':'$FUN'/0.
It is up to FormatFun to present the
selected objects of the table in a suitable way. However, if
a character list is chosen for presentation it must be an
Erlang expression that can be scanned and parsed (a trailing
dot will be added by qlc:info though).
FormatFun is called with an argument
that describes the selected objects based on optimizations
done as a result of analyzing the filters of the QLC where
the call to
qlc:table/2 occurs. The possible values of the
argument are:

{lookup, Position, Keys, NElements, DepthFun}.
LookupFun is used for looking up objects in the
table.
{match_spec, MatchExpression}. No way of
finding all possible answers by looking up keys was
found, but the filters could be transformed into a
match specification. All answers are found by calling
TraverseFun(MatchExpression).
{all, NElements, DepthFun}. No optimization was
found. A match specification matching all objects will be
used if TraverseFun is unary.

NElements is the value of the info/1,2 option
n_elements, and DepthFun is a function that
can be used for limiting the size of terms; calling
DepthFun(Term) substitutes '...' for parts of
Term below the depth specified by the info/1,2
option depth. If calling
FormatFun with an argument including
NElements and DepthFun fails,
FormatFun is called once again with an
argument excluding
NElements and DepthFun
({lookup, Position, Keys} or
all).

The value of
key_equality is to be '=:=' if the table
considers two keys equal if they match, and to be
'==' if two keys are equal if they compare equal. The
default is '=:='.